论文标题
拆分Malcev-Poisson-Jordan代数
Split Malcev-Poisson-Jordan algebras
论文作者
论文摘要
我们介绍了分裂的Malcev-Poisson-Jordan代数作为分裂Malcev Poisson代数的自然扩展，因此分裂（非交通）泊松代数。我们表明，一个分裂的malcev-poisson-jordan代数可以写成直接sum $ p = \ oplus_ {j} in J} i_j $，任何$ i_j $ a $ i_j $ a non-Zero a $ a $ p $的$ p $以某种方式满足$ [i_ {j_1}，j_1}，i_ __________________________________________________i { I_ {J_2} = 0 $对于$ J_1 \ neq J_2。$在某些条件下，表明$ P $的上述分解是通过其简单理想的家庭。
We introduce the class of split Malcev-Poisson-Jordan algebras as the natural extension of the one of split Malcev Poisson algebras, and therefore split (non-commutative) Poisson algebras. We show that a split Malcev-Poisson-Jordan algebra $P$ can be written as a direct sum $P = \oplus_{j \in J}I_j$ with any $I_j$ a non-zero ideal of $P$ in such a way that satisfies $[I_{j_1},I_{j_2}] = I_{j_1} \circ I_{j_2} = 0$ for $j_1 \neq j_2.$ Under certain conditions, it is shown that the above decomposition of $P$ is by means of the family of its simple ideals.
